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<p>We establish necessary and sufficient conditions for the existence of <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(P_\omega (Y_0,\lambda _0)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>P</mi> <mi>ω</mi> </msub> <mrow> <mo stretchy="false">(</mo> <msub> <mi>Y</mi> <mn>0</mn> </msub> <mo>,</mo> <msub> <mi>λ</mi> <mn>0</mn> </msub> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation>-solutions of a nonautonomous two-term differential equation of the fourth order with rapidly varying nonlinearity and also find asymptotic representations for these solutions and their derivatives up to the third order, inclusively.</p>

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ON THE ASYMPTOTICS OF SOLUTIONS OF A CLASS OF ESSENTIALLY NONLINEAR NONAUTONOMOUS DIFFERENTIAL EQUATIONS

  • 期刊论文

  • 发表日期：

    2025年12月1日

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  • Vyacheslav Evtukhov,
  • Sergii Golubev

摘要

We establish necessary and sufficient conditions for the existence of \(P_\omega (Y_0,\lambda _0)\) P ω ( Y 0 , λ 0 ) -solutions of a nonautonomous two-term differential equation of the fourth order with rapidly varying nonlinearity and also find asymptotic representations for these solutions and their derivatives up to the third order, inclusively.